Rotary transmission devices for a plurality of cables are known, e.g., as disclosed in U.S. Pat. No. 4,542,858. According to that specification, two spirally formed support bands are provided to carry the cables. The support bands with their band ends rolled-in as rings are anchored independently of each other around pins secured to first and second plates, respectively. The side edges of the support bands glide directly on the plates when the members are rotated relative to each other. On this occasion, the movement of the support bands is superimposed to the turning movement of the driven plate because of the contraction or widening of the spiral, whereby this plate and also the side edge of the support bands sliding along it are endangered to wear. Additionally, the support bands can twist around their fastening pins when the spiral is contracting or widening, with the result that the support band can come into mutual contact and block each other as with a band brake and that the cables are subject to bending stresses.
According to the prior art the cables are laid in a straight line along the respective support band and are fastened to it by means of straps made of plastic. As a result, the cables, which are relatively stiff, are subject to considerable tension with every movement of the spiral and with every occurrence of heat expansion or contractions.